That place? As the only female redshirt to be killed during the entire run of The Original Series. Thompson was killed in the episode "By Any Other Name" when the Kelvan Hanar turns her and another redshirt into "dehydrated porous cuboctahedron solids", which look suspiciously like sponges filled with dust or something.
Then the leader of the Kelvans, Rojan, crushes her sponge form and that's the end of Yeoman Thompson. I'm surprised that no other redshirt women were killed off in TOS. Then again, I don't think a lot of women were killed on that show. Probably didn't sit well with studio execs and censors.